Face behavior not equal after loop cut
This is because you have created non-planar faces.

A non-planar face is a face with vertices which are not aligned in a plane in any direction.

Under the hood everything is represented in triangles (at least for drawing purposes), so blender must decide how to cut the quads. It can cut them two different ways:



Which way is used appears to be decided more or less at random.

To avoid this undefined behavior, you can split non-planar faces manually to match what you want (J works well for this). You can also press 3D view > Header > Clean up > Split non-planar faces to automatically split all non-planar faces automatically: